200 L23 §5.3 Logarithmic Functions The exponential function ( )xf xa=(0,1)aa>≠is a 1-1 function and, therefore, it has the inverse 1( )fx−. We denote the inverse logaxand read “logarithm to the base aof x”. Sketch the graphs of 2xy=and 2logyx=. Sketch the graphs of 12xy⎛⎞=⎜⎟⎝⎠and 12logyx=201 We use what we know about xya=and inverses to get the properties of logayx=. ( )xf xa=1( )logafxx−=Points (0,1) and (1,)aare on the graph Points ( , ) and ( , ) are on the graph 0y=is HA Domain: (,)−∞ +∞Domain: (,) Range: (0,)+∞Range: (,) logxaax=for any real xlogaxax=for 0x>**Important** Since inverse functions undo each other with respect to composition, the following identitieshold: logfor all real xaaxx=logfor 0axaxx=>. We use these identities for solving exponential and logarithmic equations and inequalities.
has intentionally blurred sections.
Sign up to view the full version.